The U.S. Army's top commander in Europe, Lt. Gen. Ben Hodges, said Monday that his soldiers could begin training regular Ukraine army troops in November if the White House approves.

About 305 paratroopers from the 173rd Airborne Brigade based in Vicenza, Italy, have been training Ukrainian Ministry of Interior units, akin to a national guard, at the Yaroviv training ground in western Ukraine near the Polish border.

Hodges said the training of three battalions from the Ministry of Interior units would finish by mid-November. Last week, Army Chief of Staff Gen. Ray Odierno visited the Yaroviv site to observe the training.

"What is under consideration is what I would call Phase II (of training) which would begin in late November, if approved," Hodges said. "Then we would begin to train Ministry of Defense army units starting in November, but a final decision has not been made on that yet."

He noted that British troops have already begun small-scale training of Ukrainian army units in the effort to deter Russian aggression in eastern Ukraine and put pressure on Ukrainian rebels supplied and backed by Moscow to adhere to ceasefire agreements signed in February.

Hodges said the training of the Ukrainians was mutually beneficial.

"None of us has ever been under Russian artillery and rocket fire like the Ukrainians, so we also are learning from them" on counter-measures, Hodges said.

Last month, Russian President Vladimir Putin denounced the training in Ukraine and other measures taken by NATO in Eastern Europe as a direct threat to Russia and warned of retaliation.

"If someone puts some of our territories under threat, that means we will have to direct our armed forces and modern strike power at those territories from where the threat emanates," Putin said.

"As soon as some threat comes from an adjoining state, Russia must react appropriately and carry out its defense policy in such a way as to neutralise a threat against it," Putin said.

Hodges said there would be cuts to headquarters staff but "most of the major components of what's in U.S. Army Europe will remain after that cut" to 450,000.

He rejected Moscow's claims that there are no Russian troops in eastern Ukraine and that the rebels in the Donetsk and Luhansk regions were acting on their own.

"These guys are not free agents," Hodges said of the Ukrainian rebels, adding that Russia provides command and control, air defense and logistics capabilities for them. As for the presence of Russian troops in eastern Ukraine, "I have no absolutely no doubt that they're there," Hodges said.